Fractal Branching Organizations of Ediacaran Rangeomorph Fronds Reveal a Lost Proterozoic Body Plan

Fractal branching organizations of Ediacaran rangeomorph fronds reveal a lost Proterozoic body plan

Jennifer F. Hoyal Cuthill1 and Simon Conway Morris

Department of Earth Sciences, University of Cambridge, Cambridge CB2 3EQ, United Kingdom

Edited by Andrew H. Knoll, Harvard University, Cambridge, MA, and approved June 17, 2014 (received for review May 8, 2014) The branching morphology of Ediacaran rangeomorph fronds has morphology than was previously possible. These parameters are no exact counterpart in other complex macroorganisms. As such, then used to reconstruct 3D space-filling strategies within the these fossils pose major questions as to growth patterns, func- group and evaluate potential frond functions, revealing an tional morphology, modes of feeding, and adaptive optimality. adaptive radiation of fractal organizations. This provides a new Here, using parametric Lindenmayer systems, a formal model of framework for the study of growth, functional morphology, rangeomorph morphologies reveals a fractal body plan character- and evolution of these lost constructions. ized by self-similar, axial, apical, alternate branching. Consequent morphological reconstruction for 11 taxa demonstrates an adap- Results and Discussion tive radiation based on 3D space-filling strategies. The fractal body Our L-system model comprises an initial axiom (starting plan of rangeomorphs is shown to maximize surface area, consis- branch segment), production rules for axial, apical, and alternate tent with diffusive nutrient uptake from the water column (osmo- branching; and 28 parameters which together control branch trophy). The enigmas of rangeomorph morphology, evolution, and production, elongation rates, and 3D branching angles (SI Ap- extinction are resolved by the realization that they were adaptively pendix, Table S1). This incorporates both (sub) apical branch optimized for unique ecological and geochemical conditions in the production (distal extremities form the sites for subsequent late Proterozoic. Changes in ocean conditions associated with the branching) and expansion (branches grow in length and diameter Cambrian explosion sealed their fate. throughout life), based on relative branch sizes and potential ontogenetic series (4, 6, 7, 20, 21). At each step in the axial paleobiology | paleontology branching process, an apical branch segment (e.g., the tip of the stem) produces one lateral branch segment (e.g., the beginning n parallel with large-scale geochemical transitions associated of a new primary lateral branch) and an additional axis segment – – Iwith ocean oxygenation (1 3), the Ediacaran Period (635 541 (e.g., the new stem apex) (Fig. 1, SI Appendix, and Movies S1– Ma) records a major diversification of multicellular eukaryotes. S3). Lateral branches are produced alternately (e.g., left then – Rangeomorph fronds (575 541 Ma) dominated early Ediacaran right) along a branch axis. Reconstruction of overall morpholo- biotas (4) and have a characteristic branching morphology, dis- gies that closely match the anatomy of the fossils (Fig. 2 and tinct from any known Phanerozoic organism (5). Although the SI Appendix) validates this model of branching and growth. fronds are often preserved as flattened impressions, exceptional Collectively, these reconstructions demonstrate how different moldic fossils preserve details of the 3D branching structure to body shapes and symmetry patterns [characteristics relied upon a resolution of 30 μm (6). Qualitative classifications for rangeomorph branching patterns have been proposed (7, 8), but no Significance quantitative model has previously been formulated. Because branching is repeated over decreasing size scales (with up to four Rangeomorph fronds characterize the late Ediacaran Period observed orders of branching), rangeomorph fronds have been – informally described as self-similar and fractal (4–6). Although (575 541 Ma), representing some of the earliest large organ- this has potential implications for the functional optimality of their isms. As such, they offer key insights into the early evolution of multicellular eukaryotes. However, their extraordinary branch- morphologies (5, 9), the extent to which they are formally fractal ing morphology differs from all other organisms and has proved and self-similar (10, 11) has not previously been tested. Further- highly enigmatic. Here we provide a unified mathematical model more, until now, evolutionary transitions in branching patterns of rangeomorph branching, allowing us to reconstruct 3D have not been characterized within any quantitative framework. morphologies of 11 taxa and measure their functional proper- Rangeomorphs inhabited shallow to abyssal marine environ- – ties. This reveals an adaptive radiation of fractal morphologies ments (1, 8, 12 14), evidently precluding photosynthesis for most which maximized body surface area, consistent with diffusive taxa (12). Preservational features, including bending and over- nutrient uptake (osmotrophy). Rangeomorphs were adap- folding (4, 15), suggest that rangeomorphs were soft-bodied. No tively optimal for the low-competition, high-nutrient con- evidence exists for either motility or active feeding (such as ditions of Ediacaran oceans. With the Cambrian explosion in musculature, filter feeding organs, or a mouth). Consequently, animal diversity (from 541 Ma), fundamental changes in eco- rangeomorphs have been reconstructed as sessile, feeding on logical and geochemical conditions led to their extinction. organic carbon by diffusion (or possibly endocytosis) through the body surface (3, 5, 12, 16), with a large surface area to volume Author contributions: J.F.H.C. designed research; J.F.H.C. performed research; J.F.H.C. ratio aiding nutrient uptake (5, 16). The adaptive potential analyzed data; and J.F.H.C. and S.C.M. wrote the paper. of their different branching morphologies has, however, never The authors declare no conflict of interest. been quantified. This article is a PNAS Direct Submission. Here, using parametric Lindenmayer systems (L-systems) (17, See Commentary on page 12962. 18), we present a unified model to describe the branching 1To whom correspondence should be addressed. Email: [email protected]. structure of Ediacaran rangeomorph fronds. Our quantitative This article contains supporting information online at www.pnas.org/lookup/suppl/doi:10. parameters provide a far more detailed definition of frond 1073/pnas.1408542111/-/DCSupplemental.

13122–13126 | PNAS | September 9, 2014 | vol. 111 | no. 36 www.pnas.org/cgi/doi/10.1073/pnas.1408542111 Downloaded by guest on September 28, 2021 due to alternate branching on the right and left of an axis (7)], bilateral or tetraradial symmetry in apical view, and helical tor- SEE COMMENTARY sion around the main body axis (Fig. 3 and SI Appendix). Previous descriptions (following ref. 6) informally suggested that rangeomorphs possessed a shared fractal module consisting of a centimeter-scale, self-similar frondlet (conceptually similar to the primary lateral branch and associated subbranches, as formalized here). We demonstrate that rangeomorph morphologies can be reconstructed by applying approximately self-similar branch production rules (as described above) at increasingly fine scales, although these may be modified by different parameter values to give subtle variations in the level of self-similarity (SI Appendix,TableS1). These production rules apply across the branching system of the frond [sometimes called the petalodium (8)], from the stem (the 0-order branch, which produces the first-order lateral branches) to the highest order of branching (that is, from the third-order branches) (Fig. 1). This reveals that self-similarity extends beyond the frondlet, previously hypothesized to represent the basic modular unit (6). That is to say, the entire rangeomorph frond shows approximately self- similar branching, whereas the basic unit repeated throughout the frond is a cylindrical branch segment. This branch segment can be broadly related (6) to Seilacher’s concept of the fractal pneu (24). We also show that rangeomorph fronds are approximately fractal (10) with noninteger fractal dimensions of 1.6–2.4 as determined Fig. 1. Schematic L-system model of Beothukis mistakensis.(A) First three steps of the branching process. (B) Final morphology at step 38. Segment colors in- by the 3D box counting method (SI Appendix,Fig.S13). dicate relative age, from oldest (red) to youngest (light blue). Numbers indicate Shared possession of an approximately self-similar and fractal, branch order (0, stem; 1, primary; 2, secondary; 3, tertiary; and 4, quaternary). axial, apical, and alternate branching body plan supports a rangeomorph clade (Rangeomorpha, Pflug, 1972, cited in ref. 8) but significantly increases the range of diagnostic characters [pre- by some previous comparative studies (22, 23)] emerge from viously restricted to repeated fine-scale branching (8) only visible variations on a shared branching pattern. Resulting body or- in exceptionally preserved specimens]. Note that this rangeo- ganizations include alternate-symmetry (also known as glide- morph body plan does not extend to other enigmatic Ediacaran symmetry) in frontal view [superficially bilateral symmetry, offset macroorganisms, such as Swartpuntia, Ernietta (8), or Dickinsonia EVOLUTION

Fig. 2. Ediacaran rangeomorph fossils and their 3D L-system models. (A and B) Avalofractus abaculus. A reproduced with permission from ref. 4, figure 3.1. (C and D) Charnia masoni.(C) South Australia Museum specimen number P36574, described in ref. 44, image courtesy of Jim Gehling (South Australian Museum, Adelaide, Australia). (Scale bars, 1 cm.)

Hoyal Cuthill and Conway Morris PNAS | September 9, 2014 | vol. 111 | no. 36 | 13123 Downloaded by guest on September 28, 2021 This also allows much more realistic estimates of frond surface area and volume than were possible using simple geometric models (5, 16). Ratios of external surface area to tissue volume [assuming a 0.1-mm-thick metabolic tissue layer (5)] fall between 77 and 352 cm2/cm3 (SI Appendix,TableS2), within the range for osmotrophic giant bacteria (see also ref. 5). Absolute surface areas (SI Appendix, Table S2) also reach very high values. For example, in the large recliner Hapsidophyllas flexibilis the external surface area is equivalent to 58 m2 (in the same order of magnitude as the human lung). Given their large size, rangeomorphs almost certainly relied upon aerobic metabolism (29) of organic carbon (3, 5). Among the 11 studied taxa, the vast ma- jority of body surface area (>95%) is provided by the branching frond (rather than the buried holdfast, where present), and this would have maximized access to the water column. Thus, rangeomorphs most likely fed by the uptake of dissolved organic carbon (5) [or possibly small organic particles (3)], as well as oxygen, from the surrounding seawater, primarily through the surface of the branching frond [although subsidiary nutrient capture from the sediment, through the holdfast or reclining body surface, is a possibility (16, 23)]. The fractal branching of the rangeomorph frond is an optimal geometric solution to the problem of space-filling, maximizing surface area (and correspondingly nutrient uptake) within the boundaries of the total space occupied (9). The most planar of the fronds have fractal dimensions that range from 1.6 (for Avalofractus) to just below 2 (at 1.99 for Trepassia), as estimated by 3D box counting (SI Appendix,Fig.S13). Other taxa (Beothukis, Bradgatia, Culmofrons,andFractofusus andersoni) have estimated fractal dimensions above 2 (up to 2.4 for Bradgatia; SI Appendix, Fig. S13), reflecting branch arrangements which provide greater 3D space-filling. For example, the helical [lettuce-like (30)] arrangement of the primary branches in Bradgatia (Fig. 3 and SI Appendix) occupies the greatest relative bounding volume (SI Appendix, Table S2) and achieves the highest fractal dimension. Space-filling by the theoretical skeleton of the rangeo- Fig. 3. Three-dimensional space-filling by Ediacaran rangeomorph fronds morph branching frond (composed of 1D branch segments) is, (illustrated 1/2 estimated life size). Locations indicate estimated bounding therefore, so effective that its dimension approaches (or even box size in inferred life orientation (values in SI Appendix, Table S2). Frond exceeds) that of a 2D plane. In contrast to a simple plane (that colors indicate Euclidean distance-based clusters (cophenetic correlation is, an ellipse of comparable height and width), however, the coefficient = 0.77). branching frond provides up to 40 times the external surface area (SI Appendix, Table S2). Such structures (incorporating dense, planar feeding nets) maximize nutrient capture, particularly if (23). This suggests that the rangeomorphs were a distinct, high- oriented (passively or actively) with the width axis of a feeding ranking clade of multicellular eukaryotes (2, 6) and supports the net perpendicular to the ambient water current (31). view that the Ediacaran biota was far from homogenous but in- Cluster analysis of the total 3D space occupied by a repre- stead included diverse phylogenetic lineages and body plans (25). sentative of each taxon (Fig. 3 and SI Appendix, Fig. S12) sug- More widely, approximately analogous morphologies (in- gests diversification into three major space-filling strategies: cluding alternate, axial, and apical to subapical branching pat- those maximizing vertical height (Fig. 3, blue), those of more terns) are seen across the tree of life, among bacteria, protists, moderate height including some with high volume (green), and plants, fungi, and animals, so indicating extensive convergent inferred benthic recliners with an accentuated horizontal width evolution of fractal-like branching structures (26). Therefore, (red). Given that the greatest variance between taxa is in height superficially similar branching arrangements are not necessarily rather than width or depth (Fig. 3 and SI Appendix, Table S2), indicative of close phylogenetic affinity. Indeed, one of the most this suggests ecological tiering (32) and a strong selective pres- striking features of such fractal patterns is that highly detailed sure for greater height. The fluid dynamics that rangeomorphs structures can be described mathematically by quite simple rules experienced are likely to have depended on their local density (27). Correspondingly, the genetic and developmental programs and size, with a recent theoretical fluid flow model suggesting of self-similar biological structures may be comparatively simple that dense rangeomorph communities may have created specific (and conceivably require a relatively small number of genetic canopy flow conditions (16). This model predicts a strong se- changes to evolve) because emergent structural properties do lective advantage for increased height to maximize access to not, in themselves, require genetic specification (9, 11, 28). faster flowing fluid, thereby increasing nutrient absorption. Although some exceptional rangeomorph fossils do preserve Our growth model also reveals a range of mechanisms by aspects of 3D morphology (4), the nature of these casts means which modifications to a shared growth pattern can achieve that the full depth of the frond (perpendicular to the preserved different space-filling strategies (Fig. 3 and SI Appendix, Table surface) cannot be measured directly (21). However, our re- S1). For example, height can be favored via rapid production of constructions of 3D branching patterns provide estimates of primary branches at angles relatively close to vertical (e.g., overall dimensions (Fig. 3), throwing new light on frond ecology. Charnia masoni) or by a high rate of elongation for the basal

13124 | www.pnas.org/cgi/doi/10.1073/pnas.1408542111 Hoyal Cuthill and Conway Morris Downloaded by guest on September 28, 2021 stem segment (e.g., Culmofrons plumosa). To increase frond The unique rangeomorph fronds were fractal, surface area width, primary branches are produced at a less acute angle from specialists of the Ediacaran. At the Cambrian explosion, the SEE COMMENTARY the stem (e.g., Beothukis and Bradgatia). Space-filling of the third ecological and geochemical conditions to which the rangeo- dimension (i.e., adding depth if vertically oriented or height if morphs were optimized ceased to exist, and their extraordinary horizontal; Fig. 3) may also be augmented, by the helical ar- body plan was lost from life’s repertoire. rangement of the primary branches around the central axis [e.g., Beothukis (4) and Bradgatia (30)], by rotations of the primary Methods branches to form a double-layered structure [e.g., Fractofusus First, this study established a unified model for rangeomorph theoretical (15)], or via primary branch curvature (e.g., Hapsidophyllas). morphology using parametric (18) Lindenmayer (L) systems (17), written Some of the tallest rangeomorphs (Charnia and Trepassia) within the L-studio programming environment (37). L-systems are a class of appear in the oldest part of the Avalonian sequence (1, 4). As it parallel derivation grammar, in which specified production rules are applied stands, this suggests that fronds maximizing vertical height in parallel to control iterative rewriting of the axiom (a starting string, here representing the first stem segments, and holdfast if present). The symbols evolved first, followed by diversification into a wider range of 3D produced are then interpreted graphically to visualize a geometry encoded branching and space-filling strategies (Fig. 3). However, it is by the output L-system string (representing the branching system) (18). A possible that these large rangeomorphs [with Trepassia reaching branching L-system is characteristically fractal, with self-similar elements vis- more than 1 m in length (1, 4)] had smaller, and as yet unknown, ible at decreasing size scales (38). Parametric L-systems allow branching pa- precursors. Further to this, evolutionary transitions within the rameter values (such as branching angles and growth rates) to vary between Rangeomorpha should be interpreted with some caution due to branches (for example, of different orders or ages), enabling realistic repre- uncertainties regarding true paleobiogeographic and temporal sentation of biological structures with nonuniform branching patterns (18). ranges (SI Appendix, Table S3) (13). Rangeomorph morphologies were modeled using formal production rules Among the in situ communities of the earliest Avalon As- and parameters based on branching patterns of 11 studied species and quantitative measurements (of branching angles and body dimensions) from best- semblage, rangeomorphs are by far the most diverse and abun- preserved representatives (SI Appendix). For each species, the L-system output dant macroorganisms (33). Furthermore, establishment of the geometry was then processed and analyzed using Blender 2.69 and MATLAB major rangeomorph space-filling strategies (Fig. 3) preceded the (2012b; Mathworks). For measurement comparability, L-system output was appearance of a much wider range of macroorganisms (such as standardized to the same finite approximation (four orders of branching). Dickinsoniomorphs and Erniettomorphs) in the White Sea As- The fractal dimension of each modeled frond was estimated using box semblage from ∼555 Ma (34), with all included rangeomorphs counting, the method most commonly used to analyze complex fractal shapes except Rangea itself (35) first appearing in the Avalon Assem- (10). This method determines the number (n) of boxes of a given size (r) that blage, by 565 Ma (SI Appendix, Table S3). This suggests that early cover the input image. The scale (r) is incrementally decreased to determine the relationship between box size and image coverage. The slope of the line diversification of rangeomorph branching patterns effected a radi- = − ation in the key characters of body size and microhabitat [which are for this relationship gives the fractal dimension of the image D log(n)/log(r). If dimension D is not an integer, this indicates that the image is a fractal (its linked by the interaction between body size and access to fluid flow geometry does not correspond exactly to an integer dimension, i.e., a 1D (16, 33)] and was driven by ecological competition between ran- line, 2D plane, or 3D volume). The input image for 2D box counting was a 2D geomorph taxa. These features are consistent with a rapid adaptive binary (black or white) skeleton of the branching pattern, in frontal view (SI radiation shortly after the Gaskiers glaciation [from 579 Ma (1, 4)]. Appendix, Fig. S13). Input for 3D box counting was a 3D binary skeleton of Thus, evolution of the fractal branching morphology achieved un- the branching pattern (SI Appendix, Fig. S13). Two-dimensional box count- precedented body size and elevated the rangeomorphs into the new ing was conducted using ImageJ (39). Three-dimensional box counting was ecological realms of the water column, enabling diversification in conducted in MATLAB with a script incorporating the Wavefront object an environment more or less free of other macroorganisms. toolbox (40), Inhull function (41), and boxcount toolbox (42). Because 3D box counting is highly computationally intensive, two large species, Fractofusus Conclusions misrai and Pectinifrons abysallis, were analyzed using 2D box counting only. Functionally relevant frond properties were calculated from the output With their terminal Proterozoic extinction and unique mor- mesh, including the surface area to tissue volume ratio [with modeled tissue

phology, Ediacaran rangeomorph fronds have been described as depths of 0.1, 0.5, and 1 mm (comparable to ref. 5)] and the size (height, EVOLUTION a failed experiment in evolution (24). However, our analysis width, and depth) of a bounding box around the modeled organism. demonstrates that these intriguing fossils possessed a fractal Bounding box axes for each species were oriented relative to inferred life morphology which combined programmatic [and potentially position (based on fossil morphology and preservation). Dimensions for each genetic developmental (9, 11, 28)] simplicity, structural ver- species were scaled based on approximate specimen lengths recorded in the satility, and functional optimality for the uptake of organic carbon literature (SI Appendix, Table S2). A Euclidean cluster analysis of these scaled (osmotrophy) and oxygen. The appearance of rangeomorph fossils dimensions was conducted using paired group linkage in palaeontological statistics (43). (1) occurred after a move away from anoxic, sulfidic, and fer- ruginous oceans, toward conditions more favorable for aerobic ACKNOWLEDGMENTS. We thank A. Liu, J. Gehling, C. Kenchington, and M. D. macroorganisms (2, 29). Their disappearance coincides with the Brasier for discussion and making fossil casts and photographs available for Cambrian explosion in metazoan diversity, a dramatic increase study, with additional thanks to the Oxford University Museum of Natural in competition, and, crucially, decreased availability of organic History and the University of Cambridge Sedgwick Museum of Earth Sciences for access to their collections and to the South Australia Museum for providing carbon in ocean water (2, 12, 19, 24, 34, 36). These potentially specimen photographs. We also thank S. Gerber and three anonymous interacting factors suggest that the Ediacaran to Cambrian reviewers for highly constructive comments on the manuscript. This research transition was a bad time to be a sessile, soft-bodied osmotroph. was supported by Templeton World Charity Foundation Grant LBAG/143.

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